What is the stock carburetor's mm Bore on a 2003 HD FLHR RoadKing

10.5 ounces about

Sorry I do not go back quite that far but possibly there is a system relay and if so that is likey what you are looking for.

Underneath the center dash or seat there is the control module for the lights / speedo ensure that it did not come unplugged. Same problem happened to me on my 2004 Big Dog Pitbull which uses a very similiar module as your road king.

The age-old Harley stigma:Louder is better.
We all love the Harley sound but to get loud you may sacrifice performance. There are numerous after-market pipes that will improve performance and change sound but you cannot really do both. Drag pipes are the loudest but would be lousy looking on your Roadking and you lose mid-range response. Pipes have to be tuned and it is an exacting science.
Best bet is to go to J&P Cycles website and look at all the pipes. Call their tech support and ask what they recommend.
Here is an excellent web site

http://www.nightrider.com/biketech/exhaust.htm

Likely as follows:

How much wiring and just from the tach or off into the harnesses?

Try and get the carbs balanced .You may have one in need of adjusting .